Simplification of rational function

Question

I saw the following simplification done:

$$\frac{100}{\frac{900sL}{900+sL}+100}$$ is equal to $$\frac{sL + 900}{10sL + 900}$$ and was wondering how this is done?

Thank you

Answer 1

Just simple algebraic transformations $$ \frac{100}{\frac{900sL}{900+sL}+100}=\frac{100}{\frac{900sL}{900+sL}+\frac{100\left( 900+sL \right)}{900+sL}}\\=\frac{100}{\frac{1000sL+90000}{900+sL}}=100\times \frac{900+sL}{1000sL+90000}=\frac{sL+900}{10sL+900} $$

Answer 2

You could do it by first dividing numerator and denominator by $100$ to get $\dfrac{1}{\dfrac{9sL}{900+sL}+1}$

and then multiplying numerator and denominator by $900+sL$ to get $\dfrac{900+sL}{9sL+900+sL}.$

Can you take it from here?